The present invention relates to a method for highly accurate measurements of propagation characteristics, in particular, phase velocity, of leaky surface acoustic waves (LSAWs) by an ultrasonic material characterization system using a focused ultrasonic beam.
The ultrasonic material characterization system has been developed as a new substance/material property analysis/evaluation technique, and it uses ultrasonic plane waves and ultrasonic focused waves for quantitative measurements. One of the quantitative measurement schemes using the ultrasonic focused waves is a V(z) curve analysis. This scheme is to measure propagation characteristics (phase velocity and propagation attenuation) of leaky surface acoustic waves (LSAWs) excited on a water-loaded specimen surface. The measurement can be done using an ultrasonic point-focus beam (PFB) and an ultrasonic line-focus beam (LFB). Now, a description will be given of an LFB ultrasonic material characterization system (see References (1) and (2)).
The LFB ultrasonic material characterization system determines LSAW propagation characteristics on the water/specimen boundary through analysis of a V(z) curve obtained by changing the relative distance z between an LFB ultrasonic device and the specimen. The principle of measurement by the LFB ultrasonic material characterization system will be described with reference to FIG. 1, which depicts in section the system wherein an ultrasonic device composed of an ultrasonic transducer 1 and an LFB acoustic lens 2 and a specimen 4 are disposed. The coordinate system is defined with its origin at the focal point of the acoustic lens 2 in water 3 as shown. Ultrasonic plane waves excited by the ultrasonic transducer 1 are converged by the LFB acoustic lens in wedge form onto the surface of the specimen 4 through the water 3 used as a coupler. When the specimen 4 is moved away from a focal plane 5 toward the ultrasonic device, only those components of the reflected wave from the specimen 4 which propagate through the acoustic lens 2 along paths #0 and #1 approximately shown in FIG. 1 most contribute to the generation of the output from the ultrasonic transducer 1 due to the effect of the cylindrical surface of the acoustic lens 2. The component #0 is a directly reflected component from the specimen 4, and this component will hereinafter be referred to as a phasor V0(z). On the other hand, the component #1 is one that impinges on the specimen 4 at an LSAW excitation critical angle xcex8LSAW and propagates as an LSAW on the surface of the specimen 4xe2x80x94this component will hereinafter be referred to as a phasor V1(z). The phasors are given by the following equations (1) and (2) taking into account their phase and amplitude variations with the lengths z of their paths.
V0(z)=|V0(z)|exp{j(xe2x88x922kWz+xcfx860)}xe2x80x83xe2x80x83(1)
V1(z)=|V1(z)|exp{j(xe2x88x922kW cos xcex8LSAWz+xcfx861)}xe2x80x83xe2x80x83(2)
kW=2xcfx80f/VWxe2x80x83xe2x80x83(3)
where kW and VW are the wave number and velocity of a longitudinal wave in the water 3, f is an ultrasonic frequency, and xcfx860 and xcfx861 are initial phases of the phasors. The transducer output V(z) is given by the following equation as the sum of the two phasors.
V(z)=V0(z)+V1(z)xe2x80x83xe2x80x83(4)
Noting the amplitude of the transducer output signal, the amplitude V(z) of the phasor V(z) is given by the following equation (5).
V(z)=|V(z)|=|V0(z)+V1(z)|xe2x80x83xe2x80x83(5)
Therefore, the V(z) curve takes a waveform that is periodically maximized and minimized due to variations in the relative phase difference between the two phasors with the distance z, and the interference interval xcex94z of the V(z) curve is given by the following equation (6).
xcex94z=2xcfx80/k(xcex94z)=2xcfx80/2kW(1xe2x88x92cos xcex8LSAW)xe2x80x83xe2x80x83(6)
where k(xcex94z) is the wave number of the V(z) curve interference waveform on the V(z) curve. The LSAW velocity VLSAW is determined by the following equation (7) from the interference interval xcex94z of the V(z) curve.                               V          LSAW                =                              V            W                                              1              -                                                (                                      1                    -                                                                  V                        W                                                                    2                        ⁢                        f                        ⁢                                                  xe2x80x83                                                ⁢                        Δ                        ⁢                                                  xe2x80x83                                                ⁢                        z                                                                              )                                2                                                                        (        7        )            
The LSAW propagation attenuation is also obtainable from the waveform attenuation factor of the V(z) curve.
FIG. 2 is a graph showing an example of the V(z) curve measured at an ultrasonic frequency f=225 MHz for a (111) GGG (Gadolinium Gallium Garnet) specimen with LSAWs propagating in the [{overscore (1)}{overscore (1)}2] direction.
A description will be given below of the procedure for the analysis of the V(z) curve to determine the LSAW velocity VLSAW. FIG. 3 is a flowchart explaining the procedure for the V(z) curve analysis. Usually, the V(z) curve measured on a decibel scale (FIG. 4A) is converted to digital form and then read into a computer, wherein it is converted to a linear scale (step S1). A VLxe2x80x2 curve, which is an approximation of a VL(z) curve reflecting the characteristic of the ultrasonic device, is subtracted from the V(z) curve to obtain a VIxe2x80x2(z) curve (step S2). The VLxe2x80x2(z) curve used in this case is, for example, such a V(z) curve as depicted in FIG. 4B which was measured for a Teflon (trademark) specimen in which no leaky surface acoustic waves are excited.
The next step is to remove, by digital filtering, small interference components (on the V(z) curve in FIG. 4A) due to a spurious noise signal caused on the VIxe2x80x2(z) curve by a carrier leakage signal in an RF switching circuit for generating an RF tone burst signal used in the measurement system or multiple-reflected signals of ultrasonic waves in the acoustic lens (step S3). After this, interference components (interference interval xcex94z components) resulting from leaky surface acoustic waves are removed by digital filtering from the VIxe2x80x2(z) curve to synthesize a xcex94VL(z) curve representing low-frequency components including DC components (step S4). This is followed by subtracting xcex94VL(z) from VIxe2x80x2(z) calculated in step S2 to obtain such a Vl(z) curve as shown in FIG. 5A which is an interference output necessary for analysis (step S5).
The digital filtering is implemented, for example, by the moving average method. An FFT analysis of the VI(z) curve provides such a frequency spectrum distribution as depicted in FIG. 5B, and the interference interval xcex94z is obtained from the peak frequency (step S6). Since the longitudinal wave velocity VW in water is known as a function of temperature as set forth in Reference (3), it can be determined from the water temperature TW measured at the same time as the V(z) curve is measured (step S7). Therefore, the LSAW velocity VLSAW can be calculated by Eq. (7) from the interference interval xcex94z and the longitudinal wave velocity VW (step S8). While in the above the analysis scheme has been described on the assumption of only one leaky surface acoustic wave mode, it is a matter of course that when multiple modes are present, propagation characteristics can be measured for each mode. The V(z) curve in FIG. 2 is shown to have removed therefrom by the moving average method the small interference components based on the above-mentioned spurious noise signal. Thus it can be seen that the VLSAW measurement accuracy depends mainly on the water temperature measurement accuracy, which determines the longitudinal wave velocity VW, and the translation accuracy of a Z (vertical translation) stage used in the system.
Now, a description will be given of the influence of a temperature measurement error on the VLSAW measurement accuracy. FIG. 6 shows LSAW velocity measurement errors calculated by Eq. (7) with respect to water temperature measurement errors at LSAW velocities of 2000 m/s, 3000 m/s, 4000 m/s, 6000 m/s and 10000 m/s in a xc2x10.2xc2x0 C. measurement error range with the true value of water temperature set to 23xc2x0 C. From FIG. 6, it is shown that the LSAW velocity measurement with a resolution of, for example, xc2x10.002% requires the water temperature to be measured with an accuracy of xc2x10.02xc2x0 C. Incidentally, when the water temperature is 23xc2x0 C. or so, the longitudinal wave velocity linearly changes with temperature, and the rate of change is 2.83 (m/s)/xc2x0 C.
FIG. 7 depicts in block form the LFB ultrasonic material characterization system. The coordinate axes x, y and z of the system are set as shown. An RF tone burst signal 7 from a transmitter 6A in a pulse mode measurement system 6, which is electrical circuitry, is converted by the ultrasonic transducer 1 to an ultrasonic signal. The ultrasonic signal is converged by the LFB acoustic lens 2 having a cylindrical surface into wedge form for incidence on the specimen 4 through the water 3. The reflected signal from the specimen surface is converted again by the transducer 1 to an electrical signal. The converted output from the transducer 1 is provided via a directional bridge 8 to and detected by a receiver 6B in the pulse mode measurement system 6, and the detected output is converted by an A/D converter 9 to an amplitude V(z) signal or complex V(z) signal in digital form, which is stored on a data recording medium (not shown) in a computer 14.
The amplitude (in the amplitude V(z) curve measurement mode), or amplitude and phase (in the complex V(z) curve measurement mode) of the transducer output V(z) are recorded as a function of the distance z between the specimen 4 and the acoustic lens 2 while at the same time bringing the former closer to the latter relative to the focal point of the lens 2 by driving a Z stage (not shown) in a mechanical stage 12. At this time, the distance z of translation of the Z stage is measured by a laser interferometer 15, from which pulses synchronized with the translation of the Z stage are fed to the A/D converter 9. At the same time, the temperature of the water 3 is measured using a thermocouple 10 and a digital voltmeter 11.
The mechanical stage 12 comprises, in addition to the Z stage, a xcex8 (rotation) stage for measuring the dependence of LSAW propagation characteristics on the direction of propagation, an XY (horizontal translation) for measuring the distribution of LSAW velocity on the specimen surface, a tilting stage for accurate alignment between the ultrasonic device and the specimen 4, and a specimen holder provided with a vacuum-suction mechanism for firmly holding thereon the specimen 4. The XY stage, the Z stage, the xcex8 stage and the tilting stage for alignment use are each driven by a motor and placed under the control of a stage controller 13. To provide a highly stabilized temperature-measuring environment, the mechanical stage including the specimen is placed in a temperature-controlled chamber 16. The characterization system is further provided with a pure water supply/drain system 17 and a specimen loader/unloader 18 to permit supply and drain of the water 3 and replacement of the specimen 3 without opening the door of the temperature-controlled chamber 16 and hence under stabilized temperature conditions. The computer 14 controls the entire system and measures and analyzes the V(z) curve to determine the LSAW propagation characteristics.
The thermocouple 10 is disposed as close to the ultrasonic wave propagation region as possible as depicted in FIG. 7 since it cannot be directly inserted into the ultrasonic wave propagation region during measurement. In general, however, a temperature distribution exists in the water 3. This is attributable mainly to a temperature gradient in the water 3 by a temperature drop in the vicinity of the water surface due to the heat of evaporation of the water and variations in the temperature environment around the water 3 by the flow of air. On this account, the water temperature directly below the cylindrical surface of the acoustic lens 2 more or less differs from the temperature measured by the thermocouple 10. This difference becomes an error in estimating the longitudinal wave velocity VW, constituting a leading factor in decreasing the accuracy in measuring the LSAW velocity. Hence, stabilization of the temperature environment in the neighborhood of the specimen is extremely important in measuring the water temperature with high accuracy, that is, measuring the LSAW velocity with high accuracy.
For the reasons given above, the entire system is installed in a temperature-controlled room, or the entire mechanical stage including the specimen is placed in a temperature-controlled chamber to stabilize the temperature environment for measurements so as to provide increased accuracy in measuring the LSAW velocity. Moreover, it is already known in the art that when the ultrasonic device and the portion surrounding the specimen are placed in a closed or semi-closed space to minimize the flow of air to keep the atmosphere around the water supersaturated, the temperature distribution in the water is reduced to further stabilize the measurement temperature environment. In the temperature environment thus stabilized, a measurement repeatability of xc2x10.002% is attained at one fixed point on the specimen surface (see References (2) and (4)). Further, there has been proposed a method that uses a standard specimen to calibrate a temperature measurement error due to the temperature distribution in the water 3, an error in the travel of the Z stage, and an error in the absolute value of the LSAW velocity measured value owing to the frequency characteristic of the ultrasonic device used (see Reference (5)).
However, when the measurement extends over a long time (an hour or longer, for instance), the quantity of water 3 decreases due to evaporation, causing changes in the LSAW velocity measured. It is considered that this is because the water temperature distribution differs with the quantity of water. And in measurement of a two-dimensional distribution of the LSAW velocity, the measurement resolution is lower than in the measurement at one fixed point. The reason for this is considered that the temperature distribution in the water varies with a change in the temperature distribution throughout the specimen surface according to the position of placement of the specimen on the specimen holder, or a change in the temperature environment around the specimen by the translation of the XY stage in the measurement of the two-dimensional distribution of the LSAW velocity. The above-mentioned absolute calibration method using the standard specimen is based on the assumption that the specimen under measurement and the standard specimen are equal in the temperature distribution in the water, but it is not clear to which extent their temperature distributions actually agree with each other. Further, it is still unclear how much the temperature distribution in the water changes with a decrease in the quantity of water or the translation of the XY stage. Besides, it is considered that the temperature distribution in the water and its variation differ with the quantity and surface configuration of water, the kind and shape of the specimen, the measurement temperature environment, measurement conditions, the ultrasonic device configuration, or the system used.
As described above, it is not clear in the prior art what temperature distribution in the water is, and consequently, it is also unclear how the water temperature distribution affects the accuracy of the LSAW velocity measurement. In addition, under measurement conditions where the temperature difference in the water varies during measurement as in the case of measuring the two-dimensional distribution of the LSAW velocity or carrying out the measurement for a long time, it is impossible to remove errors in the LSAW velocity measurement due to the variation in the water temperature difference. Hence, the measurement accuracy of the system is insufficient to detect slight variations in elastic properties of highly homogeneous single-crystal substrates now widely used as electronic device materials.
It is therefore an object of the present invention to provide an LSAW propagation characteristics measuring method and apparatus that correct an error in the water temperature measurement caused by the temperature distribution in the water to provide increased accuracy in the LSAW velocity measurement for high-precision analysis and evaluation of material properties.
According to this invention method for high-precision measurement of LSAW propagation characteristics by the ultrasonic material characterization system, a temperature compensating parameter is obtained by pre-measuring, with a thermocouple or similar temperature measuring element, the temperature distribution in the water at one fixed point on the specimen surface under sufficiently stable water temperature conditions, and the value of temperature measured in a temperature monitoring region during the V(z) curve measurement is corrected or compensated for by the temperature compensating value to thereby detect the temperature in the ultrasonic wave propagation region with high accuracy.
Under measurement conditions where the water temperature distribution varies as in the measurement of the two-dimensional distribution of the LSAW velocity, the measured complex V(z) curve or amplitude V(z) curve is used to measure the wave number kW of the longitudinal wave in the ultrasonic wave propagation region, from which are obtained variations in the temperature of the propagation region and in the longitudinal wave velocity. More specifically, in an apparatus that has amplitude and phase measuring functions and is capable of measuring the complex V(z) curve, the wave number kW is obtained through utilization of the directly reflected signal (phasor V0(z)) from the specimen that propagates near the center axis of the acoustic lens to form the V(z) curve. Alternatively, phase information of the V(z) curve is used to obtain the wave number kW of the longitudinal wave.
In an apparatus that has no phase measuring function but is capable of measuring only the amplitude V(z) curve, the wave number kW is obtained through utilization of the interference between a carrier leakage signal in the RF switching circuit for generating an RF tone burst signal and the V(z) signal. Alternatively, the wave number kW is obtained with an electric interference method that causes interference between a continuous wave reference signal and the V(z) signal. Furthermore, the wave number kW thus obtained is used to precisely detect a temperature variation in the measurement of the two-dimensional distribution of the LSAW velocity with reference to the temperature at one fixed point on the specimen surface pre-measured under the stable temperature condition, and the thus obtained temperature variation is used to detect a change in the longitudinal wave velocity to eliminate an error in the LSAW velocity measurement.
Thus, the LSAW velocity can be measured with high accuracy even under the measurement conditions where the temperature distribution in the water varies.